## Trigonometry (11th Edition) Clone

$$\cos74^\circ=\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$ The statement is false.
$$\cos74^\circ=\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$ As $74^\circ=60^\circ+14^\circ$, $$\cos74^\circ=\cos(60^\circ+14^\circ)$$ Now we use the cosine sum identity: $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ (be extremely careful about the sign in the middle) That means $$\cos74^\circ=\cos60^\circ\cos14^\circ-\sin60^\circ\sin14^\circ$$ As you see, the sign in the middle is different: $$\cos60^\circ\cos14^\circ-\sin60^\circ\sin14^\circ\ne\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$ Therefore, the statement $$\cos74^\circ=\cos60^\circ\cos14^\circ+\sin60^\circ\sin14^\circ$$ is false.